46 EXAMPLES, 



24. A hollow cylinder, closed at both ends, is just filled 

 with water and held with its axis horizontal ; if the whole 

 pressure on its surface, including the plane ends, be three 

 times the weight of the fluid, compare the height and 

 diameter of the cylinder. Am. As 1 : 1. 



25. The side AB of a triangle ABC is in the surface of a 

 fluid, and a point D is taken in AC, such that the pressures 

 On the triangles BAD, BDC, are equal. Find the ratio 

 AD : DC. Ans. As 1 : V2 - 1. 



26. The diameters of the two pistons, p and P (Fig. 4), 

 are 2 in. and 9 in., respectively, and the smaller is 60 in. 

 above the larger. What force must be applied to the 

 smaller piston that the larger may exert a pressure of 

 1600 Ibs. ? Am. 112.8 Ibs. 



27. Compare the pressure on the area of a parabola with 

 that on its circumscribing rectangle, both being immersed 

 perpendicularly to the vertex. Ans. As 4:5. 



28. A cubical vessel is filled with two liquids, of given 

 densities, the volume of each being the same. Find the 

 pressure on the base and on any side of the vessel. 



Let a be a side of the vessel, p and p' the densities of the 

 upper and lower liquids, p' being greater than p. 



The pressure on the base = the weight of the whole 

 fluid 



The pressure on the upper half of any side 

 a 2 a 1 



To find the pressure on the lower half, replace the upper 

 liquid by an equal weight of the lower liquid, which will 

 not affect the pressure at any point of the lower half. If ' 

 be the height of this equal weight, we have 



